{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

ece340_final_fall2007_solution

# ece340_final_fall2007_solution - FALL 2007...

This preview shows pages 1–6. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: FALL 2007 (12/11/07) ECE340(Engineerir_1g Systems Analysis) Name: EU Viv MOW"; 0 Final I. (15 pts) A system is deﬁned by the input-output relationship ya) = x02) Is this system: a) (5 pts) Linear we 54‘ W = 7t. U?) 971(k): fiﬁ‘y) c) (5 pts) Causal NO . (077575/‘3” "lé: ’2. (23/779142 (71/6; 9((9L) £40 owffﬂuf C/ePCMC/S (m A 7LW’¢ Mae/W9— 02¢ 49kt 7n/7LML, FALL 2007 (12/11/07) 2. a) (10 pts) Prove the following convolution theorem. (F is the Fourier transform) F{f_:x(T)/1(f— om} : X(f)-H(f) 973) x 4% k : 30° Mamet) dz too “217 ’L) :Smﬂab WM 7% 4244‘ .013 . "87,7770? "L77 {— , 0" 1(2)€ / of?) e) {41% FALL 2007 (12/11/07) 3. a) (10 pts) Prove the following duality theorem. (F is the Fourier transform) +) {ﬁlial % F{X(t)} = x(—f) 174) 7:1ij : £31 (U r: — ’ 5 log X1405“ M 0M ./ﬁ b) (5 pts) Use the duality theorem to obtain the inverse Fourier transform of X (f) = 6(f — f0) . FALL 2007 (12/11/07) 4. (20 pts) Given the system. xm=clm ym 11(r) ——. Determine the output, Y ( f ) , for the following h(t) . a) (10 pts) h(t)= Eu: 6(t—nT) 9M XMJ—JW, WWMIL] \ﬂﬂ : {ff Maj Ir: J n : —' ( —’ "f > 71%;: f T ( Mar «en Ewe/0 M I’M/64L wee/67444:) b) (10 pts) h(t)=f_l x(T)dT Me) : f 6506/" 5 “‘79 0: M55) 6,» (zwffleﬁ g/Jh‘ﬂ J YQC) : (an)F/+ 2, JGE) ( £67m 47> a cm; fn M M 74w (Lama) FALL 2007 (12/1 l/07) 5. (10 pts) Given x[n] = cos[§n] u[n], M >1 m=l Determine the z—transform of x[n] and the region of convergence. M 1m): #671). (0} Z’n)uk(m) : go, (Lug/7n) LM“) 3 >([%') : (09(gn)_£—n /~ Cos/3'77)?" 6. (10 pts) Consider a quantizer with the following input—output relationship. N) FALL 2007 (12/11/07) 7. (15 pts) For the discrete-time system deﬁned by the following difference equation yln] = x["] — xi" — 2l a) (5 pts) Determine the impulse response h[n]. hay) : glut). 5(l’l'1)/ b) (10 pts) Plot the magnitude response ofthe system, I H(e’"') |. HLe’n/a): ’1 é'Ha-w JPN BUO/ 73w. 7 a) é ) LJ ...
View Full Document

{[ snackBarMessage ]}

### Page1 / 6

ece340_final_fall2007_solution - FALL 2007...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online